Stage 17 round 6 (#16/#17, PR C): lobby sort + server-derived in-game friend state

Lobby: group the my-games list into your-turn / opponent-turn / finished
(empty sections hidden), ordered by last activity (your-turn oldest-first,
the other two newest-first), as a compact line-separated list. gameDTO and
FB GameView gain last_activity_unix (turn start while active, finish time
once finished); a pure lib/lobbysort.ts holds the grouping/ordering.

Friends: the in-game 'add to friends' item is now server-derived via a new
GET /user/friends/outgoing (+ friends.outgoing op), returning addressees with
a pending OR declined request (both read as 'request sent'), so it is correct
across reloads; it shows a disabled '✓ in friends' once accepted. It
live-updates when the opponent answers: RespondFriendRequest now publishes
friend_added (accept) / friend_declined (new notify sub-kind, decline) to the
original requester, whose open game re-derives its friend state.

Tests: lobbysort unit test; gateway outgoing + last_activity transcode tests;
backend integration ListOutgoingRequests + respond-publishes-to-requester;
e2e updated for the new lobby section labels + a non-friend active opponent.
Docs: ARCHITECTURE notify catalog, FUNCTIONAL(+ru) lobby/friends, PLAN.

gateway/internal/transcode/transcode_social.go

@@ -13,6 +13,7 @@ import (
 const (
 	MsgFriendsList       = "friends.list"
 	MsgFriendsIncoming   = "friends.incoming"
+	MsgFriendsOutgoing   = "friends.outgoing"
 	MsgFriendRequest     = "friends.request"
 	MsgFriendRespond     = "friends.respond"
 	MsgFriendCancel      = "friends.cancel"
@@ -37,6 +38,7 @@ const (
 func registerStage8(r *Registry, backend *backendclient.Client) {
 	r.ops[MsgFriendsList] = Op{Handler: friendsListHandler(backend), Auth: true}
 	r.ops[MsgFriendsIncoming] = Op{Handler: friendsIncomingHandler(backend), Auth: true}
+	r.ops[MsgFriendsOutgoing] = Op{Handler: friendsOutgoingHandler(backend), Auth: true}
 	r.ops[MsgFriendRequest] = Op{Handler: friendRequestHandler(backend), Auth: true}
 	r.ops[MsgFriendRespond] = Op{Handler: friendRespondHandler(backend), Auth: true}
 	r.ops[MsgFriendCancel] = Op{Handler: friendCancelHandler(backend), Auth: true}
@@ -78,6 +80,16 @@ func friendsIncomingHandler(backend *backendclient.Client) Handler {
 	}
 }
 
+func friendsOutgoingHandler(backend *backendclient.Client) Handler {
+	return func(ctx context.Context, req Request) ([]byte, error) {
+		res, err := backend.ListOutgoing(ctx, req.UserID)
+		if err != nil {
+			return nil, err
+		}
+		return encodeOutgoingList(res), nil
+	}
+}
+
 func friendRequestHandler(backend *backendclient.Client) Handler {
 	return func(ctx context.Context, req Request) ([]byte, error) {
 		in := fb.GetRootAsTargetRequest(req.Payload, 0)